Solve for $x$ : $ 3|x + 8| + 9 = 2|x + 8| + 5 $
Answer: Subtract $ {2|x + 8|} $ from both sides: $ \begin{eqnarray} 3|x + 8| + 9 &=& 2|x + 8| + 5 \\ \\ { - 2|x + 8|} && { - 2|x + 8|} \\ \\ 1|x + 8| + 9 &=& 5 \end{eqnarray} $ Subtract ${9}$ from both sides: $ \begin{eqnarray} 1|x + 8| + 9 &=& 5 \\ \\ { - 9} &=& { - 9} \\ \\ 1|x + 8| &=& -4 \end{eqnarray} $ Simplify: $ |x + 8| = -4$ The absolute value cannot be negative. Therefore, there is no solution.